By Luca Mari, Leon Reznik (auth.), Dr. Leon Reznik, Dr. Vladik Kreinovich (eds.)
The lively improvement of the web and different details applied sciences have considerably improved the quantity and diversity of assets of data on hand on selection making. This ebook provides the present traits of sentimental computing functions to the fields of measurements and data acquisition. major subject matters are the construction and presentation of knowledge together with multimedia, digital setting, and computing device animation in addition to the advance of choices made at the foundation of this knowledge in a variety of functions starting from engineering to enterprise. so as to make top of the range judgements, one has to fuse info of other varieties from numerous assets with differing levels of reliability and uncertainty. the need to use clever methodologies within the research of such platforms is tested in addition to the inspiring relation of computational intelligence to its usual counterpart. This publication comprises a number of contributions demonstrating an additional stream in the direction of the interdisciplinary collaboration of the organic and machine sciences with examples from biology and robotics.
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U We can introduce distance in G(L) with the aid oflemma 1. Lemma 1. Letst, St' e metrics in L. Then G(L), s,= {,uh J1:1.. lIt}, St' = {,ul: , #l: . lIt'l, d(,u, v) - be the d(s"sn= Ld(Jlj,Jlj) j=l is the metrics in G(L). The proof of this lemma is given in [Ryjov, A. (1987)]. The semantic statements fonnulated above may be fonnalized as follows. Let s, e G(L). e. ~: G(L) ~ [0,1), satisfying the following conditions (axioms): AI. ~ s,) =0, if s, is a set of characteristic functions; A2. Let s" s'" e G(L), t and t' may be equal or not equal to each other.
Requirements 1 and 2 are quite natural for membership functions of concepts forming the scale values set of the FLS. In fact, the first one signifies that, for any concept used in the Universal set, there exists at least one object which is standard for the given concept. If there are many standards, they are positioned in a series and are not "scattered" around the Universe. The second requirement signifies that, if the objects are "similar" in the metrics sense in the Universal set, they are also "similar" in the sense of FLS.
350j [5], Appendix A, Table 17), we thus have 0'2(c:} = ~ ·21+1> . r (~+ c:) . fi/2 (see [1]), so this equality clearly holds. Differentiating both sides ofthe equality (9) with respect to c:, we conclude that 20'(c:) . O"(C:} = ~. In(2) . r (~ + c:) + 21+e: . r' (~ + c:) ). , [5]): r(z}· r (z + 4) = (211'}1/2. 21/ 2- 2z . 2. y1r' 2- 2z 2 r(z} . (13) In particular, for z = 1 + c:, we get r (~ ) = r(2+2c:} . T2e:. 2+C: r(I+c:) 2 (14) One of the main properties of a gamma function is that r(n + 1) = n· r(n)j hence r(2 + 2c:) = (1 + 2c:).